Find the mean, median, and mode of the set of values.
Age (years)
14
15
16
17
18
19
20
Frequency
4
11
16
11
8
6
5
To find the mean, median, and mode of the set of values, we first need to organize the data:
Age (years): 14, 15, 16, 17, 18, 19, 20
Frequency: 4, 11, 16, 11, 8, 6, 5
Mean:
Mean = sum of (age * frequency) / total frequency
Mean = (14*4 + 15*11 + 16*16 + 17*11 + 18*8 + 19*6 + 20*5) / (4 + 11 + 16 + 11 + 8 + 6 + 5)
Mean = (56 + 165 + 256 + 187 + 144 + 114 + 100) / 51
Mean = 1022 / 51
Mean = 20
Median:
The median is the middle value when the data is ordered. Since the frequencies add up to 51, the median will be the value at the 51/2 = 25.5th position. Since this is not a whole number, we take it to be the average of the 25th and 26th values when the data is ordered.
Ordering the data: 14, 15, 15, ..., 17, 17, 17, 17, 18, 18, ..., 20, 20
The 25th and 26th values are both 17, so the median is 17.
Mode:
The mode is the value that appears most frequently in the data set. In this case, the mode is 16 since it has the highest frequency of 16.
Therefore, the mean is 20, the median is 17, and the mode is 16.